Finite element analysis for geometrically nonlinear deformations of smart functionally graded plates using vertically reinforced 1-3 piezoelectric composite
Source abstract
Abstract
In this paper, a finite element model has been developed for the geometrically nonlinear static analysis of simply supported functionally graded (FG) plates integrated with a patch of vertically reinforced 1-3 piezoelectric composite material acting as a distributed actuator. The material properties of the functionally graded substrate plate are assumed to be graded only in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The analysis of the electro-elastic coupled problem includes the transverse deformations of the overall plate to utilize the transverse normal actuation by the distributed actuator for counteracting the nonlinear deformations of smart functionally graded plates. The nonlinear governing equations of equilibrium are solved by using direct iteration method with under-relaxation. The numerical illustrations suggest the potential use of the distributed actuator made of vertically reinforced 1-3 piezoelectric composite material for active control of nonlinear deformations of smart functionally graded plates. The effect of variation of piezoelectric fiber orientation in the distributed actuator on its control authority for counteracting the nonlinear deformations of smart functionally graded plates has also been investigated.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Aeroelasticity and Vibration Control · Structural Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (38)
Show source-provided references
1. Argyris, J., Tenek, L.: Linear and geometically nonlinear bending of isotropic and multilayered composite plates by the natural mode method. Comput. Methods Appl. Mech. Eng. 113, 207–251 (1994)
2. Bailey, T., Hubbard, J.E.: Distributed piezoelectric polymer active vibration control of a cantilever beam. J. Guid. Control Dyn. 8, 605–611 (1985)10.2514/3.20029 ↗
3. Batra, R.C., Vel, S.S.: Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J. 40, 1421–1433 (2001)
4. Baz, A., Poh, S.: Performance of an active control system with piezoelectric actuators. J. Sound Vibration 126, 327–343 (1988)10.1016/0022-460X(88)90245-3 ↗
5. Baz, A., Poh, S.: Optimal vibration control with modal positive position feedback. Opt. Control Appl. Methods 17, 141–149 (1996)10.1002/(SICI)1099-1514(199604/06)17:2<141::AID-OCA566>3.0.CO;2-D ↗
6. Crawley, E.F., Luis, J.D.: Use of piezoelectric actuators as elements of intelligent structures. AIAA J. 25, 1373–1385 (1987)10.2514/3.9792 ↗
7. Dong, S., Tong, L.: Vibration control of plates using discretely distributed piezoelectric quasi-modal actuators/sensors. AIAA J. 39, 1766–1772 (2001)10.2514/2.1507 ↗
8. Feldman, E., Aboudi, J.: Buckling analysis of functionally graded plates subjected to uniaxial loading. Composite Struct. 38, 29–36 (1997)10.1016/S0263-8223(97)00038-X ↗
9. He, X.Q., Ng, T.Y., Sivashanker, S., Liew, K.M.: Active control of FGM plates with integrated piezoelectric sensors and actuators. Int. J. Solids Struct. 38, 1641–1655 (2001)10.1016/S0020-7683(00)00050-0 ↗
10. Hellen, L.C., Kun, L., Chung, L.C.: Piezoelectric ceramic fiber/epoxy 1-3 composite for high frequency ultrasonic transducer application. Mater. Sci. Eng. B 99, 29–35 (2003)10.1016/S0921-5107(02)00444-0 ↗
11. Huang, X.-L., Shen, H.-S.: Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments. J. Sound Vibration 289, 25–53 (2006)10.1016/j.jsv.2005.01.033 ↗
12. Kawai, T., Yoshimura, N.: Analysis of large deflection of plates by the finite element method. Int. J. Numer. Methods Eng. 1, 123–133 (1969)10.1002/nme.1620010109 ↗
13. Koizumi, M.: Concept of FGM. In: Holt, B.J., Koizumi, M., Hirai, T., Munir, Z.A. (eds.) Ceramic Transaction, vol. 34, pp. 3–10. The American Ceramic Society, Westerville, OH (1993)
14. Liew, K.M., He, X.Q., Ng, T.Y., Kitipornchai, S.: Finite element piezo-thermo-elasticity analysis and active control of FGM plates with integrated piezoelectric sensors and actuators. Comput. Mech. 31, 350–358 (2003)10.1007/s00466-003-0437-0 ↗
15. Liew, K.M., He, X.Q., Ray, T.: On the use of computational intelligence in the optimal shape control of functionally graded smart plates. Comput. Methods Appl. Mech. Eng. 193, 4475–4492 (2004)10.1016/j.cma.2004.02.016 ↗
16. Loy, C.T., Lam, K.Y., Reddy, J.N.: Vibration of functionally graded cylindrical shells. Int. J. Mech. Sci. 41, 309–324 (1999)10.1016/S0020-7403(98)00054-X ↗
17. Mian, A.M., Spencer, A.J.M.: Exact solutions for functionally graded and laminated elastic materials. J. Mech. Phys. Solids 46, 2283–2295 (1998)10.1016/S0022-5096(98)00048-9 ↗
18. Miller, S.E., Hubbard, J.E.: Observability of a Bernoulli–Euler beam using PVF2 as a distributed sensor. MIT Draper Laboratory report, July 1, 1987
19. Ootao, Y., Tanigawa, Y.: Three-dimensional transient piezo-thermo-elasticity in functionally graded rectangular plate bonded to a piezoelectric plate. Int. J. Solids Struct. 37, 4377–4401 (2000)10.1016/S0020-7683(99)00257-7 ↗
20. Ootao, Y., Tanigawa Y.: Control of transient thermoelastic displacement of a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heating. Acta Mech. 148, 17–33 (2001)10.1007/BF01183666 ↗
21. Peng, F., Ng, A., Hu, Y.-R.: Actuator placement optimization and adaptive vibration control of plate smart structures. J. Intell. Mater. Syst. Struct. 16, 263–271 (2005)10.1177/1045389X05050105 ↗
22. Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998)10.1016/S0020-7683(97)00253-9 ↗
23. Ray, M.C.: Optimal control of laminated shells with piezoelectric sensor and actuator layers. AIAA J. 41, 1151–1157 (2003)10.2514/2.2058 ↗
24. Ray, M.C., Pradhan, A.K.: The performance of vertically reinforced 1-3 piezoelectric composites in active damping of smart structures. Smart Mater. Struct. 15, 631–641 (2006)10.1088/0964-1726/15/2/047 ↗
25. Ray M.C., Pradhan A.K.: On the use of vertically reinforced 1-3 piezoelectric composites for hybrid damping of laminated composite plates. Mech. Adv. Mater. Struct. 14, 245–261 (2007)10.1080/15376490600795683 ↗
26. Reddy, J.N., Cheng, Z.Q.: Three-dimensional solutions of smart functionally graded plates. ASME J. Appl. Mech. 68, 234–241 (2001)10.1115/1.1347994 ↗
27. Sankar, B.V.: An elasticity solution for functionally graded beams. Composite Sci. Technol. 61, 689–696 (2001)10.1016/S0266-3538(01)00007-0 ↗
28. Shen, H.S.: Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. Int. J. Mech. Sci. 44, 561–584 (2002)10.1016/S0020-7403(01)00103-5 ↗
29. Smith, W.A., Auld, B.A.: Modeling 1-3 composite piezoelectrics: thickness mode oscillations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 31, 40–47 (1991)10.1109/58.67833 ↗
30. Teymur, M., Chitkara, N.R., Yohngjo, K., Aboudi, J., Pindera, M.J. Arnold, S.M.: Thermoelastic theory for the response of materials functionally graded in two directions. Int. J. Solids Struct. 33, 931–966 (1996)10.1016/0020-7683(95)00084-4 ↗
31. Tiersten, H.F.: Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969)10.1007/978-1-4899-6453-3 ↗
32. Vel, S.S., Batra, R.C.: Three-dimensional analysis of transient thermal stresses in functionally graded plates. Int. J. Solids Struct. 40, 7181–7196 (2003)10.1016/S0020-7683(03)00361-5 ↗
33. Wang, B.L., Noda, N.: Design of smart functionally graded thermo-piezoelectric composite structure. Smart Mater. Struct. 10, 189–193 (2001a)10.1088/0964-1726/10/2/303 ↗
34. Wang, B.L., Noda, N.: Thermally induced fracture of a smart functionally graded composite structure. Theor. Appl. Fract. Mech. 35, 93–109 (2001b)10.1016/S0167-8442(00)00052-5 ↗
35. Woo, J., Meguid, S.A.: Nonlinear analysis of functionally graded plates and shallow shells. Int. J. Solids Struct. 38, 7409–7421 (2001)10.1016/S0020-7683(01)00048-8 ↗
36. Yang, J., Shen, H.S.: Dynamic response of initially stressed functionally graded rectangular thin plates. Composite Struct. 54, 497–508 (2001)10.1016/S0263-8223(01)00122-2 ↗
37. Yang, J., Kitipornchai, S., Liew, K.M.: Non-linear analysis of thermo-electro-mechanical behavior of shear deformable FGM plates with piezoelectric actuators. Int. J. Numer. Methods Eng. 59, 1605–1632 (2004)10.1002/nme.932 ↗
38. Zhong, Z., Shang, E.T.: Three dimensional exact analysis of a simply supported functionally gradient plate. Int. J. Solids Struct. 40, 5335–5352 (2003)10.1016/S0020-7683(03)00288-9 ↗